Metal-organic pulsed laser deposition for stoichiometric complex oxide thin films

ABSTRACT

Methods and systems for forming complex oxide films are provided. Also provided are complex oxide films and heterostructures made using the methods and electronic devices incorporating the complex oxide films and heterostructures. In the methods pulsed laser deposition is conducted in an atmosphere containing a metal-organic precursor to form highly stoichiometric complex oxides.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application is a divisional of U.S. patent application Ser.No. 16/252,783 that was filed Jan. 21, 2019, the entire contents ofwhich are incorporated herein by reference.

REFERENCE TO GOVERNMENT RIGHTS

This invention was made with government support under DE-FG02-06ER46327awarded by the US Department of Energy. The government has certainrights in the invention.

BACKGROUND

Complex oxide systems have attracted scientific focus for plenty ofinteresting physics and emergent phenomena including ferroelectricity,ferromagnetism, and superconductivity. For practical applications,fabrication and characterization of thin films and theirheterostructures have been intensively studied. However, even if thinfilms are grown epitaxially on proper substrates, their quality is ofteninferior to bulk single crystals. Non-equilibrium thin-film growthconditions lead to non-stoichiometry and additional point defects,whilst most single crystal growth is under near-equilibrium conditions.An analogous near-equilibrium synthesis process for complex oxide thinfilms would result in materials with low concentration of point defects,opening pathways to new functionalities.

Pulsed laser deposition (PLD) is one of the most widespread methods ofcomplex oxide thin film growth, primarily because of the accuratetransfer of target composition to the films, and sharp interfaces ofresulting heterostructures. However, the non-equilibrium nature of PLDgrowth leads to a density of point defects much larger than thatrequired to observe quantum phenomena in most materials systems.Recently, a hybrid MBE process using Sr metal and TTIP gas as sourcematerials showed a growth window yielding stoichiometric SrTiO₃ films.(B. Jalan, et al., Appl. Phys. Lett. 95, 032906 (2009); B. Jalan, etal., J. Vac. Sci. Technol. A 27, 461 (2009); and J. Son, et al., Nat.Mater. 9, 482 (2010).) La-doped SrTiO₃ films grown with this hybrid MBEprocess exhibited electron mobilities of ˜32,000 cm²V⁻¹s⁻¹ at lowtemperature, higher than that of electron-doped bulk SrTiO₃ singlecrystals. (J. Son, et al., 2010 and A. Spinelli, et al., Phys. Rev. B.81, 155110 (2010).) A PLD-based near-equilibrium process woulddramatically expand the range of low-defect materials andheterostructures due to the ease of incorporating with existingwide-ranging PLD growth schedules.

SUMMARY

Methods for forming complex oxide films are provided. Also provided arecomplex oxide films and heterostructures made using the methods andelectronic devices incorporating the complex oxide films andheterostructures. Some embodiments of the heterostructures aretwo-dimensional electron gas-forming heterostructures.

One embodiment of a method for forming a complex oxide film includes thesteps of: providing a deposition substrate and at least one metal oxidetarget comprising a first cation metal and oxygen in a depositionchamber; introducing a metal-organic precursor comprising a secondcation metal and oxygen into the deposition chamber; and laser ablatingthe metal oxide target using a pulsed laser in the presence of themetal-organic precursor to generate a flux of the metal oxide, whereinthe metal oxide and the metal and oxygen from the metal-organicprecursor are sequentially deposited onto the deposition substrate toform a layered complex oxide film.

One embodiment of a two-dimensional electron gas-forming heterostructureincludes: a DyScO₃ substrate or a GdScO₃ substrate; a tensilely strainedSrTiO₃ film on the DyScO₃ substrate or the GdScO₃ substrate; and aLaAlO₃ film on the tensilely strained SrTiO₃ film, wherein atwo-dimensional electron gas is formed at the interface between theSrTiO₃ film and the LaAlO₃ film.

One embodiment of a two-dimensional electron gas-forming heterostructureincludes: a (LaAlO₃)_(0.3)—(Sr₂AlTaO₆)_(0.7) substrate or a NdGaO₃substrate; a compressively strained SrTiO₃ film on the(LaAlO₃)_(0.3)—(Sr₂AlTaO₆)_(0.7) substrate or the NdGaO₃ substrate; anda LaAlO₃ film having a thickness of 9 unit cells or fewer on thecompressively strained SrTiO₃ film, wherein a two-dimensional electrongas is formed at the interface between the SrTiO₃ film and the LaAlO₃film.

Other principal features and advantages of the invention will becomeapparent to those skilled in the art upon review of the followingdrawings, the detailed description, and the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

Illustrative embodiments of the invention will hereafter be describedwith reference to the accompanying drawings, wherein like numeralsdenote like elements.

FIG. 1 depicts a schematic of a metal-organic pulsed laser depositionsystem. In addition to PLD system with high pressure RHEED, gas supplysystems are combined.

FIG. 2A, panels (a)-(f) and FIG. 2B depict physical processes of STOfilm growth and corresponding atomic structures by conventional PLD andMOPLD. FIG. 2A, panels (a)-(c), show the physical process during STOfilm growth in conventional PLD. FIG. 2A, panel (a) shows that the fluxof SrTiO_(3-δ), SrO_(x). TiO_(y) is supplied on TiO₂-terminated STOsubstrate by pulsed laser ablation of a STO target. FIG. 2A, panel (b)shows the film growth on the substrate. Note that there is no drivingforce to achieve perfect cation stoichiometry. The cation stoichiometryis mainly governed by the flux ratio of Sr/Ti. FIG. 2A, panel (c) showsthat after the film growth, non-stoichiometric STO is formed. FIG. 2A,panels (d)-(f) show the physical process during STO film growth inMOPLD. FIG. 2A, panel (d) shows that SrO_(x) flux is supplied by pulsedlaser ablation of a SrO target. TTIP is simultaneously supplied but notadsorbed on TiO₂-terminated STO surface. FIG. 2A, panel (e) shows thatTTIP is only adsorbed and decomposed to form TiO₂ layer on top ofSrO-terminated STO, which results in FIG. 2A, panel (f), perfectstoichiometry by self-regulation. FIG. 2B shows the schematics depictingthermodynamic consideration for selective adsorption of TTIP in logP_(TTIP) vs. 1/T (K⁻¹) diagram. Above each dashed line, TTIP adsorptionon TiO₂- or SrO-terminated STO is energetically favorable. Between thetwo lines (shaded region), a selective adsorption of TTIP onSrO-terminated surface occurs, resulting in the growth of stoichiometricSTO films.

FIG. 3A-FIG. 3C depict structural analysis of STO films grown by MOPLD.FIG. 3A shows out-of-plane θ-2θ XRD patterns of STO films on (001) STOsubstrates. (002) peak positions of off-stoichiometric STO films andSr₂TiO₄ are indicated by the grey and black arrows, respectively. FIG.3B shows Raman spectra of STO films on (001) STO substrates at 10 K.Data from Sr-rich, stoichiometric, Ti-rich STO (determined by XRD) filmsare represented in the two lower traces, three middle traces, and twoupper traces, respectively. FIG. 3C shows normalized TO₄ intensity inRaman spectra (FIG. 3B) as a function of TTIP inlet pressure. Becausethe sample grown at 9 and 10 mTorr has Sr₂TiO₄ phase, those samples wereexcluded in this plot. The shaded area is a stoichiometric growth windowdetermined by Raman spectra at 10 K.

FIG. 4A-FIG. 4C depict electrical properties of 2DEG in LAO/STOinterfaces. FIG. 4A shows temperature dependence of electron mobility atthe interface of LAO 5 u.c./(001) STO substrate and LAO 5u.c./MOPLD-grown STO 12 u.c./(001) STO substrate. TTIP gas inletpressures of 15-23 mTorr were employed for growing STO 12 u.c. films.FIG. 4B shows electron mobility at 2 K in LAO 5 u.c./MOPLD-grown STO 12u.c./(001) STO substrate as a function of TTIP gas inlet pressure.Structural growth window determined by Raman (FIG. 3C) is represented bythe shaded area. FIG. 4C shows SdH oscillation of LAO 5 u.c./MOPLD-grownSTO 12 u.c./(001) STO substrate where TTIP gas inlet pressure of 21mTorr was used for the STO 12 u.c. film.

FIG. 5A-FIG. 5D depict depth-resolved cathodoluminescence spectroscopymeasurement of STO films. FIG. 5A shows DRCLS Spectra of LAO 5u.c./MOPLD-grown STO 12 u.c./(001) STO substrate where TTIP gas inletpressure of 15, 21 mTorr was used for the STO 12 u.c. films,respectively. The probe beam voltage of 0.3 kV was used for detectingthe signals from MOPLD-grown STO film. FIG. 5B shows spectradeconvoluted using 10 Gaussian curves with the constant baseline. Defectfeatures of 1.6, 1.7, 1.9, 2.1, 2.4, 3.0 eV, an indirect band gap of3.25 eV, a direct bandgap of 3.6 eV, and upper conduction bands fromTi-3d splitting of 4.0 and 4.3 eV were identified. Note that Ti-3dorbital related conduction band features at 3.6 eV, 4 eV, and 4.3 eV arevirtually identical when normalized in the STO substrate. FIG. 5C showsrelative defect concentration of STO films as a function of TTIP gasinlet pressure during the growth. Each defect area of Ti_(Sr) ²⁺, V_(o)²⁺, Ti³⁺ was normalized with respect to the bandgap area near 3.6 eV.FIG. 5D shows relative oxygen vacancy density across the interfaces.

FIGS. 6A-6C show current-voltage curves for a LAO/STO/STOheterostructure (FIG. 6A), a LAO/STO/LSAT heterostructure (FIG. 6B), anda LAO/STO/DSO heterostructure (FIG. 6C).

DETAILED DESCRIPTION

Methods and systems for forming complex oxide films are provided. Alsoprovided are complex oxide films and heterostructures made using themethods and electronic devices incorporating the complex oxide films andheterostructures.

One embodiment of a method of forming a complex oxide film includes thesteps of: (a) providing a deposition substrate and at least one metaloxide target in a deposition chamber, the at least one metal oxidetarget comprising a first cation metal and oxygen; (b) introducing ametal-organic precursor comprising a second cation metal and oxygen intothe deposition chamber; and (c) laser ablating the metal oxide targetusing a pulsed laser in the presence of the metal-organic precursor togenerate a flux of the metal oxide from the metal oxide target. In thismethod, the ablated metal oxide serves as the source of the first cationmetal, and the metal-organic precursor serves as the source of thesecond cation metal in the growing complex oxide film. This method, inwhich PLD is conducted in an atmosphere containing a metal-organicprecursor, is referred to herein as MOPLD. As illustrated in theExample, the methods can be used to form films of SrTiO₃ (STO) from SrOtargets and titanium-containing metal-organic precursor molecules, suchas titanium tetraisopropoxide. However, a wide variety of complex oxidescan be made using the methods by selecting the appropriate target metaloxides and metal-organic precursors.

The methods provide near-equilibrium growth conditions that result in areduced cation point defect concentration and, therefore, improvedstoichiometric growth of complex oxide films, relative to complex oxidefilms grown using more conventional techniques. As demonstrated in theExample, complex oxide films having a lower oxygen vacancy concentrationthan their corresponding bulk oxide can be grown. The stoichiometriccomplex oxides can be grown within a wide range of metal-organicprecursor fluxes and, since the pulsed laser deposition target containsoxygen, without the need for a separate dedicated oxygen source. Thisenables the use of deposition systems that are more compact and lessexpensive than conventional complex oxide growth systems.

Complex metal oxides include two or more metal cations and oxygen. Thecomplex metal oxides made using the methods described herein have alayered structure in which layers of a first cation metal and oxygenalternate with layers of a second cation metal and oxygen. A variety ofmetal oxides can be grown using the methods, including metal oxides thatare insulators, ferromagnets, antiferromagnets, piezoelectrics, andsuperconductors.

One embodiment of a system for carrying out the growth of a complexoxide film is shown in FIG. 1. The system includes a deposition chamber102 that houses a substrate 104 on which the complex oxide film is grownand at least one pulsed laser deposition (PLD) target 106. The systemfurther includes a laser 108, such as an excimer laser, configured todirect a laser beam 110 onto the surface of the PLD target to enable thetarget material, generating a target material plume 112 comprising metaloxide species.

The PLD targets are made of a target material that includes at least onecation metal of the complex oxide to be grown and oxygen. However, thePLD target does not include all of the elements of the complex oxidefilm to be grown and, therefore, is not a stoichiometric target of thetype used in conventional PLD.

If more than one type of complex oxide film is to be grown, depositionchamber 102 can house a plurality of different PLD targets thatcorrespond to the different complex oxides. As illustrated in FIG. 1,the different PLD targets can be provided on a rotating and/ortranslating PLD target carousel 114 configured to allow each of thetargets to move in and out of the path of laser beam 110.

A metal-organic precursor source is provided in fluid communication withthe deposition chamber to allow for the introduction of a metal-organicprecursor into deposition chamber 102 during the PLD of the PLD target.For example, the metal-organic precursor source may be in fluidcommunication with the deposition chamber via one or more gas injectors116. Gas injector 116 is configured to direct a flux of themetal-organic precursor 118 toward the surface of substrate 104.Additional gas injectors can be used to introduce additional organicprecursors. These organic precursors may include additional metal atomsand/or dopant atoms to grow complex oxide films containing more than twometals and/or doped complex oxide films. For example, organic precursorsincluding a dopant atom, such as nitrogen, can be introduced into thedeposition chamber during the PLD of the target oxide. By way ofillustration, tetrakis(dimethylamido)titanium (TDMAT) can be used as adopant precursor along with the TTIP to grow nitrogen-doped STO films.

The deposition system may also include a heat source in thermalcommunication with substrate 104 in order to heat the substrate to anannealing temperature and/or to maintain the substrate at a selectedcomplex oxide film deposition temperature. For example, the heat sourcecould be a second laser 120 that directs a second laser beam 121 ontosubstrate 104 or a substrate holder, as shown in FIG. 1. Alternatively,the heat source could be a heating element in physical contact withsubstrate 104 or a substrate holder. Optionally, a RHEED systemincluding a RHEED gun 122 and RHEED screen 124, configured to monitorthe growth of the complex oxide film, can be included in the depositionsystem. One or more pumps 126, 128 are used to reduce the pressure inthe deposition chamber to a pressure suitable for the deposition of thecomplex oxide film.

Because the deposition methods do not rely on a separate oxygen source,such as a plasma source or an O₂ tank, to provide oxygen, the depositionof the complex oxide can be done in an oxygen-free or substantiallyoxygen-free environment. It may be very difficult or impossible toremove all oxygen from the deposition chamber; therefore, the depositionchamber can be considered substantially free of oxygen if the oxygenpartial pressure in the chamber is 1×10⁻⁶ torr or lower and, moretypically, much lower (for example, in the range from 1×10⁻⁸ to 1×10⁻⁹torr, or lower.

An initial stage in the growth of the complex oxide film is thedeposition of a layer of the PLD target oxide onto the surface of thesubstrate from the target material plume to form a surface that isterminated by the metal oxide of the PLD target. For example, during thegrowth of an STO film, a SrO PLD target can be used to form anSrO-terminated surface. The next layer in a layered complex oxide canthen be formed via adsorption-controlled deposition of the second cationmetal and oxygen on the metal oxide terminated surface via thedecomposition of the metal-organic precursor. By way of illustration,during the growth of the STO film, a TTIP precursor can be used todeposit titanium and oxygen to form a TiO₂ layer on the previouslydeposited terminal SrO layer. Without intending to be bound to anyparticular theory of the invention, a proposed adsorption-controlledgrowth mechanism is shown in FIG. 2A. The deposition should be conductedat a temperature at which the metal-organic precursor preferentiallyadsorbs and decomposes on the metal oxide previously deposited from thePLD target (FIG. 2A, panel (e)) and preferentially desorbs from themetal oxide previously deposited from the metal-organic precursor (FIG.2A, panels (d) and (e)). This adsorption-controlled growth illustratedin FIG. 2A, panels (d)-(f), enables cation stoichiometry to bemaintained in the growing film throughout the growth process. Moreover,the near-equilibrium nature of the MOPLD process makes it possible toachieve stoichiometric complex oxide growth over a wide range ofmetal-organic precursor flux conditions. The growth stages can continueiteratively until a complex oxide film having the desired thickness isformed.

The deposition process can be carried out for a time sufficient to growa complex oxide film having a desired thickness. This includes ultrathinfilms having thicknesses of 20 unit cells (u.c.) or fewer. For example,the films can have a thickness in the range from 4 u.c. to 20 u.c.However, thicker films can also be grown.

The substrates on which the complex oxide films are grown can becomposed of bulk crystals having the same complex oxide composition asthe films. For example, STO can be deposited on the (001) face of a bulkSTO single crystal. However, the complex oxide films also can be grownon substrates of different materials. Thus, the present methods allowfor the formation of complex oxide films on a variety of substrates thatare commonly used in the electronics industry. For example, an STO filmcould be deposited on bulk (001) silicon (Si), (001)(LaAlO₃)_(0.3)—(Sr₂AlTaO₆)_(0.7) (LSAT), (110) NdGaO₃ (NGO), (110)DyScO₃ (DSO), and (110) GdScO₃ (GSO). Depending upon the lattice matchbetween the growth substrate and the complex oxide, the complex oxidefilms may be grown in an unstrained state or in a strained state,including compressive and tensile strain states. Generally, thesubstrates should be selected to have a sufficiently low latticemismatch with the complex oxide film that strain-induced defects areavoided or minimized in the film. In addition, the substrate should bechemically compatible with the complex oxide film—that is, it should notreact with the complex oxide in a way that significantly degrades thechemical and/or physical properties of the complex oxide film. Notably,the present methods can be used to fabricate heterostructures with a2DEG at an interface even when the complex oxide film is under a tensilestrain or when the complex oxide film is under a compressive strain andthe overlying complex oxide has a critical thickness for 2DEG formationthat is less than 10 u.c. As illustrated in the examples, the criticalthickness for 2DEG formation in some embodiments of the compressivelystrained heterostructures can be less than 8 u.c., less than 6 u.c., orequal to 5 u.c.

Because the complex oxide films can be formed with the sameconcentration or a lower concentration of point defects than their bulkcrystal counterparts, heterostructures that were previously grown onlyon bulk crystals of the complex oxides can now be grown on the thincrystalline complex oxide films. In the heterostructures, the variousmaterial layers that are formed on the complex oxide films can be formedusing the methods described herein or by other known depositiontechniques. Examples of heterostructures that can be grown on aninsulating complex oxide film are two-dimensional electron gas(2DEG)-forming heterostructures. These heterostructures are insulatingoxide bilayers that include a complex oxide film, as described herein,and an overlying film of a second complex oxide, wherein a 2DEG isformed at the polar/non-polar oxide interface of the two oxides. Such2DEG-forming heterostructures are useful in a variety of electronicdevices, including field-effect transistors and non-volatile memoryelements.

As illustrated in the Example, one heterostructure that forms a 2DEG atan oxide interface and that can be fabricated via MOPLD is theLaAlO₃/STO (LAO/STO) interface, which is of significant interest to theelectronics industry. LAO/STO heterostructures having an electronmobility of 10³ cm²/V·s or higher (e.g., in the range from 10³ cm²/V·sto 10⁴ cm²/V·s) at temperatures of 20 K or lower (e.g., in the rangefrom 2 to 20 K) can be fabricated. Such high mobilities are indicativeof the very high quality of the STO films. In fact, the electronmobilities in the 2DEGs that are formed by growing a second oxide on acomplex oxide film can be even higher than the electron mobilities in2DEGs that are formed by growing the same second oxide on a bulk complexoxide substrate under the same growth conditions. Such high mobilitiescan be achieved with high charge carrier densities, including chargecarrier densities of 10¹³ or higher.

Although much of the discussion provided above and in the example belowuses STO films to illustrate the deposition methods, it should beunderstood that the methods can be used to form other complex oxides byusing different PLD targets and different metal-organic precursors.Examples of metal oxide target materials include target materials thathave the formula MO_(x), where M represents a metal atom and x can be,for example, in the range from 1 to 2. Other target metal oxides includethose that have the formula M_(1-x)M″_(x)O, where M and M″ are twodifferent cation metals and 0<x<1, although x can have a value outsideof this range. Complex metal oxides that can be made from these targetsinclude those that have the formula MM′O₃ and M_(1-x)M″_(x)O₃.

By way of illustration only, BaTiO₃, CaTiO₃, and SnTiO₃ films can bedeposited using BaO, CaO, and SnO, respectively, as target materials andTTIP (with or without TDMAT) as a metal-organic precursor;Ba_(1-x)Sr_(x)TiO₃ films can be deposited using Ba_(1-x)Sr_(x)O as atarget material and TTIP (with or without TDMAT) as a metal-organicprecursor; SrVO₃ and BaVO₃ films can be deposited using SrO and BaO,respectively, as target materials and vanadium(V) oxytrisopropoxide as ametal-organic precursor; SrZrO₃ and BaZrO₃ can be deposited using SrOand BaO, respectively, as target materials and zirconium (IV)tetra-butoxide as a metal-organic precursor; and SrHfO₃ and BaHfO₃ filmscan be deposited using SrO and BaO, respectively, as target materialsand hafnium (IV) tetra-butoxide as a metal-organic precursor. Guidancefor the selection of other metal-organic precursors can be provided byreferring to the chemical vapor deposition (CVD) literature. Suitablesubstrates upon which these and other complex oxide films can be growninclude YAlO₃, LaAlO₃, NdGaO₃, LaGaO₃, LSAT, STO, DyScO₃, GdScO₃, andPrScO₃ substrates.

EXAMPLES

Example 1: This example illustrates the defect-free synthesis ofLaAlO₃/SrTiO₃ quantum heterostructures via the MOPLD growth technique,which uses TTIP as a Ti source during laser ablation of a SrO target. Astoichiometric growth window of STO for a wide flux range of TTIP makesfor a robust deposition process. The defect reduction was quantified bymeasuring an electron mobility at the interface of LaAlO₃/MOPLD-grownSrTiO₃ higher than that at a LaAlO₃/bulk SrTiO₃ substrate interface.Clean Shubnikov-de Haas oscillations were measured, a signature ofhigh-mobility arising from low defect concentration.

A comparison of SrTiO₃ film growth by conventional PLD and MOPLD isshown in FIG. 2A panels (a)-(c) and FIG. 2A panels (d)-(f),respectively. The PLD growth mechanism is complex, but recent in-situanalysis of the ablation plume showed that not only SrTiO_(3-x) species,but also SrO and TiO_(y) are separately transferred from the target tothe substrate during conventional PLD growth (FIG. 2A, panel (a)). (S.Wicklein, et al., Appl. Phys. Lett. 101, 131601 (2012).) Duringconventional PLD laser ablation, supersaturation and growth of SrTiO₃occur on the substrate. Laser fluence and spot size affect the degree ofsupersaturation, which determines the stoichiometry of the films (FIG.2A, panels (b) and (c)). (T. Ohnishi, et al., J. Appl. Phys. 103, 103703(2008).)

During MOPLD, the total working pressure should be low enough tominimize the gas phase reaction of TTIP so that surface reaction of TTIPis dominant (FIG. 2A panel (d)). In addition, the growth temperatureshould be high enough to enable TTIP adsorption on a SrO-terminatedSrTiO₃ surface while it is desorbed from a TiO₂-terminated SrTiO₃surface (FIG. 2A, panel (e)). Under such conditions, TTIP will bedecomposed on top of a SrO-terminated SrTiO₃ surface only, resulting inthe growth of stoichiometric SrTiO₃ (FIG. 2A, panel (f)). The Arrheniusbehavior of adsorption means that the reaction curve would be a line inlog P_(TTIP) vs. 1/T diagram as shown in FIG. 2B. The stoichiometricgrowth window then lies between the upper and lower dashed lines.

Based on this concept, 25-unit cell thick SrTiO₃ thin films were grownon (001) SrTiO₃ substrates by the MOPLD method. The laser conditions forSrO flux were fixed while TTIP flux was varied and controlled by a gaspressure feedback system. Details of film growth are provided below.FIG. 3A shows out-of-plane θ-2θ XRD patterns of SrTiO₃ films vs. TTIPinlet pressure. Since the SrTiO₃ lattice parameter is highly sensitiveto its stoichiometry, lattice parameters different from those of thesingle crystal substrate value arise from cation off-stoichiometry. Thedata indicate that there is a stoichiometric SrTiO₃ growth window withinthe wide range of TTIP gas inlet pressures from 11 to 21 mTorr. In thisregion, SrTiO₃ film peaks overlap those of the SrTiO₃ single crystalsubstrate, indicating stoichiometric films. At lower TTIP gas inletpressure (9 and 10 mTorr), both off-stoichiometric SrTiO₃ and a Sr₂TiO₄second phase were detected by XRD. The layer-by-layer growth mode ofSrTiO₃ growth was monitored with in-situ reflective high electron energydiffraction (RHEED). In addition, an atomic force microscopy (AFM) imageof the surface of the SrTiO₃ film after the growth shows a step-terracestructure. SrTiO₃ films were also grown on(LaAlO₃)_(0.3)(Sr₂TaAlO₆)_(0.7) (LSAT) substrates with the MOPLD method.These films exhibited a full width at half maximum value of 0.021° in anX-ray diffraction rocking curve, giving evidence to high crystalquality, and were fully coherent to the LSAT substrate. Hence, the MOPLDmethod is applicable to both strained and unstrained films.

Variable-temperature Raman spectroscopy was performed to investigate anysignature of inversion symmetry breaking due to point defects. SrTiO₃ isa cubic perovskite (space group Pm-3m) with 12 optical phonon modes.Because these phonon modes have odd symmetry with respect to theinversion center, 1^(st) order Raman peaks are not present in the idealSrTiO₃ structure. Any point defects which break inversion symmetry ofSrTiO₃ can thus be detected by 1^(st) order peaks in Raman spectra, forinstance the LO₃ or TO₄ modes. The Raman spectra of SrTiO₃ filmsmeasured at 10 K are shown in FIG. 3B. It was noted that the intensityof the LO₃ and TO₄ peaks in Ti-rich SrTiO₃ films was higher than forSrTiO₃ films within the stoichiometric growth window. The normalizedintensity I_(TO) ₄ /I_(2nd order) was used to quantitatively compare the1^(st) order peak intensities (FIG. 3C). Again, within the 11 to 21mTorr TTIP gas inlet pressure range, I_(TO) ₄ /I_(2nd order) values weresignificantly lower than that of SrTiO₃ films grown at higher TTIP gasinlet pressures. Notably, the normalized 1^(st) order peak intensitieswithin the growth window determined by XRD show small variations,whereas the XRD results are not distinguishable. For example, the 11mTorr film has a statistically significant difference in 1^(t) orderpeak intensities compared with those grown at TTIP gas inlet pressurerange from 12 to 21 mTorr. This indicates that low temperature Ramanspectroscopy is more sensitive to SrTiO₃ structural changes than XRD,especially in the SrO-rich region.

Using the SrTiO₃ films as templates, epitaxial LaAlO₃ layers were grownon SrTiO₃ by a conventional PLD to investigate the effect of thereduction in point defects on properties of the interfacial 2DEG. Thefilm thicknesses of LaAlO₃ and SrTiO₃ were fixed at 5 u.c. and 12 u.c.,respectively, with TTIP growth pressures spanning the stoichiometricgrowth window. The RHEED patterns and oscillations of each layer wereobtained. The highest electron mobility of ˜6,260 cm²/V·s at 2 K was forthe SrTiO₃ film that was grown under 21 mTorr TTIP gas inlet pressure(FIG. 4A). This value is substantially higher than that in theLaAlO₃/SrTiO₃ substrate, 2,400 cm²/V·s, where the LaAlO₃ layer wasprepared by the same growth condition. At low temperatures, in highmagnetic fields and high electron mobility, the resistance R_(xx) willoscillate as B is swept, giving rise to Shubnikov-de Haas (SdH)oscillations. FIG. 4C shows clear SdH oscillations for the sample grownat 21 mTorr TTIP gas inlet pressure, indicating a low level of defectconcentration. From the SdH oscillations, a partial carrier density of1.7×10¹² cm⁻², an effective mass of 1.0 m_(e) (m_(e) is the bareelectron mass), and a quantum mobility of the order of 1500 cm²/V·s canbe extracted, consistent with or much better than the values reportedfor LaAlO₃ grown under optimized conditions on a bulk single-crystallineSrTiO₃. (A. D. Caviglia, et al., Phys. Rev. Lett. 105, 236802 (2010).)Interestingly, the defect concentration, i.e. related to the electronmobility, seems to be dependent on the level of TTIP inlet, and itmonotonically decreases with increasing TTIP pressure within thestructural growth window, as shown in FIG. 4B. This indicates that pointdefect concentration varies within the structural growth window,resulting in dramatic mobility enhancement.

Depth-resolved cathodoluminescence (DRCLS) was performed to directlymeasure the point defects and their distribution in MOPLD-grown SrTiO₃films. FIG. 5A shows DRCLS spectra of the LaAlO₃/MOPLD-grownSrTiO₃/SrTiO₃ samples where SrTiO₃ films were grown at the TTIP inletpressure of 15 and 21 mTorr, respectively. The 0.3 kV beam energy wasused for the measurement to collect data from the SrTiO₃ film regions.There is a clear difference in intensities of two samples at the energyrange from ˜1.5 to ˜3.4 eV where the spectra were normalized withrespect to the band gap (3.6 eV) peak intensity. Each spectrum wasdeconvoluted using 10 Gaussian curves (FIG. 5B), and the area of eachdefect was normalized with respect to the area of the band gap peak. Thedata fit as a superposition of contributions from previously identifiedsources. (D. Lee, et al., Phys. Rev. Mater. 2, 060403(R) (2018).) InFIG. 5C, relative point defect densities of Ti_(Sr) ²⁺, V_(O) ²⁺, andTi³⁺ are plotted for different TTIP inlet pressures for MOPLD-grownSrTiO₃ film in the LaAlO₃/SrTiO₃/SrTiO₃ heterostructure. As the TTIPinlet pressure is increased, the amount of Ti_(Sr) ²⁺ is increased,whereas the amount of V_(O) ²⁺ is decreased. This result is alsosupported by density functional theory (DFT) calculation. From the phasediagram as a function of chemical potential of Sr, Ti, and O, theformation energy of V_(O) ²⁺ and Ti_(Sr) ²⁺ could be calculated as afunction of Δμ_(O). When a higher TTIP flux is employed during theSrTiO₃ growth, the relative chemical potential of Sr is decreased whilethose of Ti and O are increased, since a single TTIP molecule possessesnot only one Ti atom but also four oxygen atoms. Thus, for asimplification, for a constant μ_(Ti) condition, the Δμ_(O) can be takenproportionally to the amount of TTIP during the growth. Thus, whenΔμ_(O) is increased, the formation energies of V_(O) ²⁺ and Ti_(Sr) ²⁺get smaller and larger, respectively, supporting the DRCLS results.Although both V_(O) ²⁺ and Ti_(Sr) ²⁺ act as scattering centers at lowtemperature, larger electron mobilities with higher TTIP flux wereobserved, as shown in FIG. 4B. This dependence of mobility on TTIP inletpressure implies that the total amount of V_(O) ²⁺ and Ti_(Sr) ²⁺decreases with increasing TTIP flux during growth. The fact that theamount of Ti³⁺ is also lower in the higher TTIP inlet pressure region(FIG. 5C) is another piece of indirect evidence of decreased totalnumber of positively charged defects in the STO films. From the depthprofile of the oxygen vacancy index, it was further confirmed that theamount of oxygen vacancies in the STO film which was grown using TTIPinlet pressure of 21 mTorr was even smaller than that in the STO bulksingle crystal (FIG. 5D).

The origin of point defect concentration variation within the structuralgrowth window by thermodynamics was also considered. It is proposed thatadjusting the TTIP pressure amounts to tuning the chemical potential ofTiO_(2-x) in the system, as discussed above. STO is known to be a linecompound in the binary system of SrO and TiO₂, but in the very narrowcomposition range at the vicinity of STO, there should exist some degreeof solubility due to entropy of mixing.

The Gibbs-Duhem relationship for μ_(TiO2-x) can be described as follows.μ_(TiO2-x) =−SdT+VdP  (1)

In this experiment, the growth temperature was fixed at 900° C. so thatthe dG/dP value was always positive, indicating that the chemicalpotential of TiO_(2-x) decreases with decreasing partial pressure ofTTIP. Therefore, the equilibrium Sr/Ti ratio in STO thin films isdetermined by the relative position between the free energy curve of STOand the chemical potential of TiO_(2-x). When the TTIP gas inletpressure is too low, the tangential line meets Sr₂TiO₄, as observed forsamples grown at 9 and 10 mTorr. If the TTIP gas inlet pressure is high,such as when 21 mTorr was used, the equilibrium composition of STO isslightly shifted to the Ti-rich side, which results in the formation ofmore Ti_(Sr) ²⁺. This is not due to the relative Ti chemical potentialincrease; rather, the resulting Ti_(Sr) ²⁺ increase may be directlyrelated to the formation of a solid-solution between Ti and Sr at theTi-rich side. Again, for this reason, the amount of V_(O) ²⁺ isdecreased, consistent with the higher mobility at the interface ofLaAlO₃/MOPLD-grown SrTiO₃.

Methods

Thin film fabrication. Single crystalline SrTiO₃ (001) substrates wereused for this study. SrTiO₃ substrates were soaked in DI-water for 30min and in buffered-BHF for 1 min to make a TiO₂-terminated surface. Bysubsequent annealing at 1000° C. for 6 h in 1 atm O₂ atmosphere, anatomically smooth surface could be obtained. In the MOPLD process, TTIPgas served as a working gas during a laser ablation of a SrO singlecrystal target. A KrF excimer laser (λ=248 nm) was used with ˜0.7 J/cm²of energy fluence and 2 Hz of repetition rate on the SrO target. TTIPgas was supplied by a gas injector and variable leak valves, where TTIPgas inlet pressure was controlled by a capacitance manometer vacuumgauge. During the SrTiO₃ film growth, the substrate temperature was keptat 900° C., and any other gas except TTIP was introduced in the chamber.The sample thickness was evaluated from RHEED oscillations. After thegrowth of the SrTiO₃ film, samples were cooled down to 600° C., and thenoxygen gas was backfilled with ˜600 Torr for the post-annealing. ForLaAlO₃ layers, the conventional PLD method was employed. The growthtemperature, oxygen partial pressure, energy fluence, and repetitionrate for LaAlO₃ were 750° C., 7.5×10⁻⁵ Torr, ˜1.0 J/cm², and 1 Hz,respectively. After the growth, samples were annealed at 600° C. in ˜150Torr of O₂ for 1 h in order to achieve equilibrium oxygen concentration.

XRD measurement. The crystal structure of samples was analyzed by ahigh-resolution four-circle XRD machine (Bruker D8 advance) using CuKα1radiation.

Raman spectroscopy measurement. Raman spectra were measured using aHoriba Jobin Yvon T64000 triple spectrometer equipped with aliquid-nitrogen-cooled multichannel charge-coupled device detector.Spectra were recorded in backscattering geometry in the temperaturerange of 10-300 K, using a variable temperature closed cycle Hecryostat. The 325 nm line of a He—Cd laser line was used for excitation;laser power density was below 0.5 W/mm² at the sample surface, lowenough to avoid any noticeable local heating. The TO₄ peak (at ˜550cm⁻¹) was used for analysis of symmetry breakdown due to point defects,since this peak was the most distinctive and did not overlap with thesecond order features. The ratio of the integrated intensity of the TO₄peak to that of the 2^(nd) order peak at 620 cm⁻¹ (plotted in FIG. 3C)was used to determine the stoichiometric growth window.

Electrical characterization. The SdH measurements were performed using afour-probe Van der Pauw method with ultrasonically wire-bonded aluminumwires as electrodes. A CRYOGENIC cryogen-free measurement system wasemployed to characterize the temperature-dependent SdH oscillations in aperpendicular magnetic field up to 16 T at low temperatures from 1.8-3.1K in steps of 0.2 K. The amplitude of the quantum oscillations atdifferent temperatures was extracted from these measurements bysubtracting a 2^(nd) order polynomial background. The data analysis isbased on the method published elsewhere. (A. D. Caviglia, et al., Phys.Rev. Lett. 105, 236802 (2010) and Y. Z. Chen, et al., Nat. Commun. 4,1371 (2013).)

Depth-Resolved Cathodoluminescence Spectroscopy Measurement and Analyses

Theoretical calculations. For the calculation of defects, the densityfunctional theory (DFT) band structure approach was used, as implementedin the Vienna ab initio simulation package (VASP). (G. Kresse, et al.,Phys. Rev. B 59, 1758 (1999); ibid B 54, 11169 (1996).) The projectedaugmented wave (PAW) method was used to approximate the electron-ionpotential. (P. E. Blöchl, Phys. Rev. B 50, 17953 (1994).) To treatexchange and correlation effects, both the local density approximation(LDA) and the semi-empirical LDA+U method were used within arotationally invariant formalism, for a better description of thelocalized transition metal d electrons. (J. P. Perdew, et al., Phys.Rev. B 23, 5048 (1981); Vladimir I Anisimov, et al., J. Phys. Condens.Mat. 9, 767 (1997); and S. L. Dudarev, et al., Phys. Rev. B 57, 1505(1998).) Here, (U−J)=5 eV was chosen for the 3d orbitals of Ti atoms, asthis value of U provides good description of the lattice parameters. Thecalculated lattice constant is 3.9 Å, similar to that measuredexperimentally, and the band gap is 2.4 eV and includes defect states.Defect calculations were performed in 135 atoms in a 3×3×3 cubicsupercell. After creating one such defect in the perfect supercell, theinternal coordinate was relaxed until the Hellman-Feynman forces wereless than 0.01 eV/Å. In the calculation, a kinetic energy cutoff of 340eV was used as the kinetic energy cutoff, and a 6×6×6 Monkhorst-Packgrid of k points Brillouin zone integration was used. (HendrikMonkhorst, et al., Phys. Rev. B 13, 5188 (1976).) In all calculations,the spin polarization was turned on to include the effect of the localmoment introduced by defect. To create an ionized (charged) defect,electrons were added to or removed from the system, and a compensatingjellium background was included. Formation enthalpy of the defect D isenergy cost to add (remove) an atom of charge q to (from) an otherwiseperfect host and is calculated using relation:ΔHf(D,q)=E(D,q)−E_(H)+μ_(removed)−μ_(added)+q(E_(V)+E_(F)), where E(D,q)is the energy of the host with the defect, E_(H) is energy withoutdefect, and E_(F) is the electrochemical potential of the charge q thatis usually measured with respect to the host valence band maximum(E_(V)).

Example 2: LAO/STO/STO, LAO/STO/LSAT, and LAO/STO/DSO heterostructureswere also grown, and their current-voltage (I-V) characteristics weremeasured to establish that electrically conductive interfaces can beformed for unstrained complex oxide films, tensile strained complexoxide films, and compressive strained complex oxide films having acritical thickness for 2DEG formation of less than 10 u.c.

STO films were grown on (001) STO, (001) LSAT, and (001) DSO substrates.12 u.c. thick STO layers were fabricated by MOPLD, using the proceduresdescribed in Example 1. Then 5 u.c. thick LAO layers were grown byconventional PLD (using a LAO single crystal as a target). For I-Vcharacteristics, samples were mounted and connected to chip carriers byaluminum wire-bonding. Two probe measurement was performed for measuringI-V curves after making a contact between chip carriers and probe tips.The I-V curves for the LAO/STO/STO, LAO/STO/LSAT, and LAO/STO/DSOheterostructures are shown in FIGS. 6A, 6B, and 6C, respectively. Theseresults demonstrate that electrically conductive interfaces, 2DEG, wereachieved for each of the heterostructures.

The word “illustrative” is used herein to mean serving as an example,instance, or illustration. Any aspect or design described herein as“illustrative” is not necessarily to be construed as preferred oradvantageous over other aspects or designs. Further, for the purposes ofthis disclosure and unless otherwise specified, “a” or “an” means “oneor more.”

The foregoing description of illustrative embodiments of the inventionhas been presented for purposes of illustration and of description. Itis not intended to be exhaustive or to limit the invention to theprecise form disclosed, and modifications and variations are possible inlight of the above teachings or may be acquired from practice of theinvention. The embodiments were chosen and described in order to explainthe principles of the invention and as practical applications of theinvention to enable one skilled in the art to utilize the invention invarious embodiments and with various modifications as suited to theparticular use contemplated. It is intended that the scope of theinvention be defined by the claims appended hereto and theirequivalents.

What is claimed is:
 1. A 2DEG-forming heterostructure comprising: a(LaAlO₃)_(0.3)−(Sr₂AlTaO₆)_(0.7) substrate or a NdGaO₃ substrate; acompressively strained SrTiO₃ film on the(LaAlO₃)_(0.3)−(Sr₂AlTaO₆)_(0.7) substrate or the NdGaO₃ substrate; anda LaAlO₃ film having a thickness of 9 unit cells or fewer on thecompressively strained SrTiO₃ film, wherein a 2DEG is formed at theinterface between the SrTiO₃ film and the LaAlO₃ film.
 2. Theheterostructure of claim 1, wherein the substrate is the(LaAlO₃)_(0.3)−(Sr₂AlTaO₆)_(0.7) substrate.
 3. The heterostructure ofclaim 2, wherein the LaAlO₃ film has a thickness in the range from 5unit cells to 9 unit cells.
 4. The heterostructure of claim 1, whereinthe SrTiO₃ film has a thickness of 20 unit cells or lower.
 5. Theheterostructure of claim 1, wherein the substrate is the NdGaO₃substrate.
 6. The heterostructure of claim 5, wherein the LaAlO₃ filmhas a thickness in the range from 5 unit cells to 9 unit cells.
 7. Theheterostructure of claim 5, wherein the SrTiO₃ film has a thickness of20 unit cells or lower.